Let's denote the number of 10-cent coins as $x$, the number of 20-cent coins as $3x$, and the number of 50-cent coins as $8x$, based on the ratio given (1 : 3 : 8).

Now, let's calculate the total value of the coins in terms of $x$:

• Value of 10-cent coins: $10x$ cents.
• Value of 20-cent coins: $20(3x) = 60x$ cents.
• Value of 50-cent coins: $50(8x) = 400x$ cents.

The total value of all the coins is the sum of these values:

$10x + 60x + 400x = 470x \text{ cents}$

We know the total value of the coins is $18.80, which is 1880 cents. Therefore, we can set up the equation:

$470x = 1880$

Now, solve for $x$:

$x = \frac{1880}{470} = 4$

Thus, $x = 4$.

Now, the number of 50-cent coins is $8x$:

$8x = 8 \times 4 = 32$

So, there were 32 fifty-cent coins in the purse.

Would you like more details or have any questions?

Here are 5 related questions you might find interesting:

1. If the ratio had been 2 : 3 : 5 instead, what would be the number of 50-cent coins?
2. How would the total value change if the number of each type of coin were doubled?
3. What would be the total value if the number of 20-cent coins was increased by 5?
4. How many coins in total are there in the purse?
5. What is the average value of a coin in the purse?

Tip: Understanding ratios can simplify problems involving proportional distributions.